Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T07:41:14.941Z Has data issue: false hasContentIssue false
  • English
  • Français

A physics-based approach to flow control using system identification

Published online by Cambridge University Press:  07 June 2012

Aurelien Hervé ,
Denis Sipp ,
Peter J. Schmid  and
Manuel Samuelides
Aurelien Hervé
Affiliation:
ONERA - The French Aerospace Lab, 8 rue des Vertugardins, 92190 Meudon, France
Denis Sipp
Affiliation:
ONERA - The French Aerospace Lab, 8 rue des Vertugardins, 92190 Meudon, France
Peter J. Schmid*
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique, 91128 Palaiseau, France
Manuel Samuelides
Affiliation:
ONERA - The French Aerospace Lab, 2 av. Edouard Belin, 31055 Toulouse, France
*
†Email address for correspondence: peter@ladhyx.polytechnique.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Control of amplifier flows poses a great challenge, since the influence of environmental noise sources and measurement contamination is a crucial component in the design of models and the subsequent performance of the controller. A model-based approach that makes a priori assumptions on the noise characteristics often yields unsatisfactory results when the true noise environment is different from the assumed one. An alternative approach is proposed that consists of a data-based system-identification technique for modelling the flow; it avoids the model-based shortcomings by directly incorporating noise influences into an auto-regressive (ARMAX) design. This technique is applied to flow over a backward-facing step, a typical example of a noise-amplifier flow. Physical insight into the specifics of the flow is used to interpret and tailor the various terms of the auto-regressive model. The designed compensator shows an impressive performance as well as a remarkable robustness to increased noise levels and to off-design operating conditions. Owing to its reliance on only time-sequences of observable data, the proposed technique should be attractive in the design of control strategies directly from experimental data and should result in effective compensators that maintain performance in a realistic disturbance environment.

JFM classification

Flow Control: Flow Control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 702 , 10 July 2012 , pp. 26 - 58
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Akers, J. C. & Bernstein, D. S. 1997 ARMARKOV least-squares identification. Proc. Am. Contr. Conf. 186–190.CrossRefGoogle Scholar
2. Akervik, E., Hoepffner, J., Ehrenstein, U. & Henningson, D. S. 2007 Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. J. Fluid Mech. 579, 305–314.CrossRefGoogle Scholar
3. Antoulas, A. C. 2005 Approximation of Large-Scale Dynamical Systems. Advances in Design and Control , Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
4. Bagheri, S., Brandt, L. & Henningson, D. S. 2009 Input/output analysis, model reduction and control of the flat-plate boundary layer. J. Fluid Mech. 620, 263–298.CrossRefGoogle Scholar
5. Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 1–50.CrossRefGoogle Scholar
6. Barkley, D., Gomes, M. G. M. & Henderson, R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
7. Blackburn, H. M., Barkley, D. & Sherwin, S. J. 2008 Convective instability and transient growth in flow over a backward-facing step. J. Fluid Mech. 603, 271–304.CrossRefGoogle Scholar
8. Cattafesta, L., Williams, D. R., Rowley, C. W. & Alvi, F. 2003 Review of active control of flow-induced cavity resonance. AIAA Paper 2003-3567.Google Scholar
9. Dergham, G., Sipp, D. & Robinet, J.-C. 2011 Accurate low dimensional models for deterministic fluid systems driven by uncertain forcing. Phys. Fluids 23 (9), 094101.Google Scholar
10. Efe, M. O. & Ozbay, H. 2003 Proper orthogonal decomposition for reduced order modelling: 2D heat flow. IEEE Conf. Contr. Appl. 2, 1273–1277.Google Scholar
11. Gibson, J. S., Lee, G. H. & Wu, C. F. 2000 Least-squares estimation of input/output models for distributed linear systems in the presence of noise. Automatica 36 (10), 1427–1442.CrossRefGoogle Scholar
12. Glowinski, R. 2003 Finite element methods for incompressible viscous flow. In Handbook of Numerical Analysis (ed. Ciarlet, P. G. & Lions, J. L. ). Numerical Methods for Fluids (Part 3) , vol. 9. pp. 3–1176. Elsevier.Google Scholar
13. Huang, S.-C. & Kim, J. 2008 Control and system identification of a separated flow. Phys. Fluids 20 (10), 101509.Google Scholar
14. Juang, J. N. & Pappa, R. S. 1985 An eigensystem realization algorithm for modal parameter identification and model reduction (control systems design for large space structures). J. Guid. Control Dyn. 8, 620–627.CrossRefGoogle Scholar
15. Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.CrossRefGoogle Scholar
16. Ljung, L. 1999 System Identification: Theory for the User, 2nd edn. Prentice Hall.Google Scholar
17. Ma, Z., Ahuja, S. & Rowley, C. W. 2010 Reduced-order models for control of fluids using the eigensystem realization algorithm. Theor. Comput. Fluid Dyn. 25, 1–15.Google Scholar
18. Marquet, O., Sipp, D., Chomaz, J.-M. & Jacquin, L. 2008 Amplifier and resonator dynamics of a low-Reynolds-number recirculation bubble in a global framework. J. Fluid Mech. 605, 429–443.CrossRefGoogle Scholar
19. Moore, B. 1981 Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans. Autom. Control 26 (1), 17–32.CrossRefGoogle Scholar
20. Penrose, R. 1955 A generalized inverse for matrices. Proc. Camb. Phil. Soc. 51, 406–413.Google Scholar
21. Rowley, C. W. 2005 Model reduction for fluids, using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15 (5), 255–289.Google Scholar
22. Rowley, C. W., Colonius, T. & Murray, R. M. 2004 Model reduction for compressible flows using POD and Galerkin projection. Physica D 189, 115–129.Google Scholar
23. Safonov, M. G. & Chiang, R. Y. 1989 A Schur method for balanced-truncation model reduction. IEEE Trans. Autom. Control 34 (7), 729–733.CrossRefGoogle Scholar
24. Samimy, M., Debiasi, M., Caraballo, E., Ozbay, H., Efe, M. O., Yuan, X., DeBonis, J. & Myatt, J. H. 2003 Development of closed-loop control for cavity flows. AIAA Paper 2003-4258.Google Scholar
25. Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J. & Myatt, J. H. 2007 Feedback control of subsonic cavity flows using reduced-order models. J. Fluid Mech. 579, 315–346.CrossRefGoogle Scholar
26. Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open flows: a linearized approach. Appl. Mech. Rev. 63 (3), 030801.Google Scholar